Chessboard Pawn-Pawn game
There is an 8*8 chessboard and two chess players having a single pawn each. A player has to move his pawn in each turn, either one step forward or one step diagonally only when this move kills the other pawn. The player who is unable to make any move loses.
Given row and column numbers of white and black pawns. The task is to predict who would win assuming both plays optimally. Note that White plays first and a pawn cannot move outside the chessboard.
Examples:
Input: rowW = 2, colW = 2, rowB = 3, colB = 3
Output: White
Input: rowW = 2, colW = 2, rowB = 3, colB = 3
Output: White
Approach:
- If its white pawn’s turn we have to check whether white pawn is on the 8th row then black wins because white pawn has no further move. If it’s black pawn’s turn then we have to check whether it is on the 1st row then white wins because black pawn has no further move.
- If its white pawn’s turn and black pawn is adjacent diagonally then white pawn will kill black pawn and white pawn wins else white pawn will move one step forward (if not already occupied by the black pawn) else white will lose.
- If it’s black pawn’s turn and white pawn is adjacent diagonally then black pawn will kill white pawn and black pawn wins else black pawn will move one step forward (if not already occupied by the white pawn) else black will lose.
Below is the implementation of the above approach:
C++
// C++ implementation of the approach #include <bits/stdc++.h> using namespace std; // Function that returns true if white wins bool whiteWins( int rowW, int colW, int rowB, int colB) { int white = 0, black = 0; while (1) { // If white can move if (rowW != 8) { // If white pawn can kill black pawn // White wins if (rowB == rowW + 1 && (colB == colW - 1 || colB == colW + 1)) return true ; // Make the move forward else rowW++; } // White has no moves // White loses else return false ; // If black can move if (rowB != 1) { // If black pawn can kill white pawn // White loses if (rowB == rowW + 1 && (colB == colW - 1 || colB == colW + 1)) return false ; // Make the move forward else rowB--; } // Black has no moves // White wins else return true ; } // If white has got more moves if (white > black) return true ; return false ; } // Driver code int main() { int rowW = 2, colW = 2, rowB = 3, colB = 3; if (whiteWins(rowW, colW, rowB, colB)) cout << "White" ; else cout << "Black" ; return 0; } |
Java
// Java implementation of the approach class GFG { // Function that returns true if white wins static boolean whiteWins( int rowW, int colW, int rowB, int colB) { int white = 0 , black = 0 ; boolean flag= true ; while (flag) { // If white can move if (rowW != 8 ) { // If white pawn can kill black pawn // White wins if (rowB == rowW + 1 && (colB == colW - 1 || colB == colW + 1 )) return true ; // Make the move forward else rowW++; } // White has no moves // White loses else return false ; // If black can move if (rowB != 1 ) { // If black pawn can kill white pawn // White loses if (rowB == rowW + 1 && (colB == colW - 1 || colB == colW + 1 )) return false ; // Make the move forward else rowB--; } // Black has no moves // White wins else return true ; } // If white has got more moves if (white > black) return true ; return false ; } // Driver code public static void main(String args[]) { int rowW = 2 , colW = 2 , rowB = 3 , colB = 3 ; if (whiteWins(rowW, colW, rowB, colB)) System.out.println( "White" ); else System.out.println( "Black" ); } } // This code is contributed by Arnab Kundu |
Python3
# Print implementation of the approach # Function that returns true if white wins def whiteWins(rowW, colW, rowB, colB): white = 0 ; black = 0 ; while ( 1 ): # If white can move if (rowW ! = 8 ): # If white pawn can kill black pawn # White wins if (rowB = = rowW + 1 and (colB = = colW - 1 or colB = = colW + 1 )): return True ; # Make the move forward else : rowW + = 1 ; # White has no moves # White loses else : return False ; # If black can move if (rowB ! = 1 ): # If black pawn can kill white pawn # White loses if (rowB = = rowW + 1 and (colB = = colW - 1 or colB = = colW + 1 )): return False ; # Make the move forward else : rowB - = 1 ; # Black has no moves # White wins else : return Frue; # If white has got more moves if (white > black): return True ; return False ; # Driver code if __name__ = = '__main__' : rowW, colW = 2 , 2 ; rowB, colB = 3 , 3 ; if (whiteWins(rowW, colW, rowB, colB)): print ( "White" ); else : print ( "Black" ); # This code is contributed by Rajput-Ji |
C#
// C# implementation of the approach using System; public class GFG { // Function that returns true if white wins static bool whiteWins( int rowW, int colW, int rowB, int colB) { int white = 0, black = 0; bool flag= true ; while (flag) { // If white can move if (rowW != 8) { // If white pawn can kill black pawn // White wins if (rowB == rowW + 1 && (colB == colW - 1 || colB == colW + 1)) return true ; // Make the move forward else rowW++; } // White has no moves // White loses else return false ; // If black can move if (rowB != 1) { // If black pawn can kill white pawn // White loses if (rowB == rowW + 1 && (colB == colW - 1 || colB == colW + 1)) return false ; // Make the move forward else rowB--; } // Black has no moves // White wins else return true ; } // If white has got more moves if (white > black) return true ; return false ; } // Driver code public static void Main(String []args) { int rowW = 2, colW = 2, rowB = 3, colB = 3; if (whiteWins(rowW, colW, rowB, colB)) Console.WriteLine( "White" ); else Console.WriteLine( "Black" ); } } /* This code contributed by PrinciRaj1992 */ |
Javascript
<script> // JavaScript implementation of the approach // Function that returns true if white wins function whiteWins(rowW , colW , rowB , colB) { var white = 0, black = 0; var flag = true ; while (flag) { // If white can move if (rowW != 8) { // If white pawn can kill black pawn // White wins if (rowB == rowW + 1 && (colB == colW - 1 || colB == colW + 1)) return true ; // Make the move forward else rowW++; } // White has no moves // White loses else return false ; // If black can move if (rowB != 1) { // If black pawn can kill white pawn // White loses if (rowB == rowW + 1 && (colB == colW - 1 || colB == colW + 1)) return false ; // Make the move forward else rowB--; } // Black has no moves // White wins else return true ; } // If white has got more moves if (white > black) return true ; return false ; } // Driver code var rowW = 2, colW = 2, rowB = 3, colB = 3; if (whiteWins(rowW, colW, rowB, colB)) document.write( "White" ); else document.write( "Black" ); // This code contributed by aashish1995 </script> |
Output:
White
Time Complexity: O(1) as the time is constant.
Auxiliary Space: O(1)
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